complete ultrafilter

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• Ultrafilter — In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged (as a filter). An ultrafilter may be considered as a finitely additive measure. Then every subset of X is …   Wikipedia

• Strongly compact cardinal — In mathematical set theory, a strongly compact cardinal is a certain kind of large cardinal number; their existence can neither be proven nor disproven from the standard axioms of set theory.A cardinal kappa; is strongly compact if and only if… …   Wikipedia

• Vopěnka's principle — In mathematics, Vopěnka s principle, named after Petr Vopěnka, is a large cardinal axiom.Vopěnka s principle asserts that for every proper class of binary relations (with set sized domain), there is one elementarily embeddable into another.… …   Wikipedia

• Singular cardinals hypothesis — In set theory, the singular cardinals hypothesis (SCH) arose from the question of whether the least cardinal number for which the generalized continuum hypothesis (GCH) might fail could be a singular cardinal.According to Mitchell (1992), the… …   Wikipedia

• Boolean-valued model — In mathematical logic, a Boolean valued model is a generalization of the ordinary Tarskian notion of structure or model, in which the truth values of propositions are not limited to true and false , but take values in some fixed complete Boolean… …   Wikipedia

• Boolean algebras canonically defined — Boolean algebras have been formally defined variously as a kind of lattice and as a kind of ring. This article presents them more neutrally but equally formally as simply the models of the equational theory of two values, and observes the… …   Wikipedia

• Ultralimit — For the direct limit of a sequence of ultrapowers, see Ultraproduct. In mathematics, an ultralimit is a geometric construction that assigns to a sequence of metric spaces Xn a limiting metric space. The notion of an ultralimit captures the… …   Wikipedia

• metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… …   Universalium

• Filter (mathematics) — The powerset algebra of the set {1,2,3,4} with the upset colored green. The green elements make a principal ultrafilter on the lattice. In mathematics, a filter is a special subset of a partially ordered set. A frequently used special case is the …   Wikipedia

• Tychonoff's theorem — For other theorems named after Tychonoff, see Tychonoff s theorem (disambiguation). In mathematics, Tychonoff s theorem states that the product of any collection of compact topological spaces is compact. The theorem is named after Andrey… …   Wikipedia

• Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …   Wikipedia